## Can Prestidigitation color people’s skin?

The Prestidigitation spell in D&D 3.5 specifically says that it is possible to use it to color items (see SRD). Given the wording, “items” can be interpreted either as “inanimate object” or more generally as “physical entity”. It’s therefore not clear if the spell can be used to color a person’s face (for example, as a joke, or as a rough disguise). The fact that the spell description reports that the saving throw is “see text”, but nothing is actually said in the text leaves me even more baffled.

## Removing imperfections in circle with color gradient edge

I am trying to draw a red circle with a colour gradient fading into white on the edge. The way I am currently doing it is to first define a smooth step function and draw a rectangular block with a color gradient defined by the smooth step function:

smoothstep[x_] := Piecewise[{{0, x <= -(1/2)}, {-20*(x + 1/2)^7 + 70*(x + 1/2)^6 - 84*(x + 1/2)^5 + 35*(x + 1/2)^4, -(1/2) < x < 1/2}, {1, x >= 1/2}}]  img = Rasterize[DensityPlot[smoothstep[x], {x, 0, 4}, {y, -4, 4}, ColorFunction -> Function[{x, y}, Hue[1, x, 1]], Frame -> False, PlotRangePadding -> None] 

which seems to be successful

Then I applied this colour gradient to a circle as a texture

ParametricPlot[{r*Cos[t], r*Sin[t]}, {r, 0, 1}, {t, 0, 2 Pi}, Mesh -> False, BoundaryStyle -> None, Axes -> False, Frame -> False, PlotStyle -> {Opacity[1], Texture[img]}] 

which is mostly successful, apart from 1) the white dot at the centre of the circle, and 2) the faint concentric red line outside.

How do I remove these imperfections in the resulting image? Should I change my approach?

## Increasing point size in 3D + color plot

I have a “4D” plot (3D + color) that I want to increase the point size of the points. Seems easy enough right? Just use the following is what I thought:

PlotStyle -> PointSize[0.01] 

However, whenever I add this to my code, it makes all the color from my “4th” dimension go away and just turns into one uniform color. How do I get past this?

Also! I’ve had people help me here on Stack Exchange to get to the code I am posting so a lot of credit goes to them for the 3d + color plot. ðŸ™‚

Here is my code and a picture of the plot that I want the point sizes to be increased.

normdSi =    Table[(p - Min[Sidata1[[All, 2]]])/(Max[Sidata1[[All, 2]]] -        Min[Sidata1[[All, 2]]]), {p, Sidata1[[All, 2]]}]; colorsSi = Table[ColorData["BlueGreenYellow"][d], {d, normdSi}]; Si4dplot =   ListPointPlot3D[{#[[3 ;; 5]]} & /@ Sidata1, PlotStyle -> colorsSi,    AxesLabel -> {"q", "\!$$\*SuperscriptBox[\(s$$, $$2$$]\)",      "\[Alpha]"}, ImageSize -> Full, LabelStyle -> {18},    ViewPoint -> {-2, -.7, 0}, PlotLabel -> Style["Si", 24]] 

Here is my data:

{{0, 0.00586554, 1.85613, 4.76551*10^-28, 5.26926}, {1, 0.00586038,    1.85857, 0.00496208, 5.26553}, {2, 0.00583292, 1.86694, 0.00737286,    5.28264}, {3, 0.00578611, 1.88105, 0.00995626, 5.31438}, {4,    0.00572788, 1.90041, 0.0195179, 5.34518}, {5, 0.0056491, 1.92576,    0.026371, 5.3971}, {6, 0.00555664, 1.95654, 0.0357567, 5.4579}, {7,    0.005454, 1.99256, 0.0488175, 5.52469}, {8, 0.00533414, 2.03443,    0.0587529, 5.61315}, {9, 0.00520924, 2.08121, 0.0728039,    5.70511}, {10, 0.00507624, 2.13333, 0.0868532, 5.80991}, {11,    0.00493048, 2.19114, 0.0969574, 5.937}, {12, 0.00479085, 2.25265,    0.111276, 6.06199}, {13, 0.00464483, 2.31891, 0.12169,    6.20612}, {14, 0.00449348, 2.3895, 0.12767, 6.36945}, {15,    0.00435635, 2.46022, 0.134399, 6.52873}, {16, 0.00421573, 2.53408,    0.13467, 6.70861}, {17, 0.00408066, 2.60798, 0.130038,    6.89764}, {18, 0.003962, 2.67731, 0.122165, 7.08088}, {19,    0.0038446, 2.74659, 0.107359, 7.27855}, {20, 0.0037445, 2.80767,    0.0891022, 7.46372}, {21, 0.00366125, 2.85969, 0.0685708,    7.63264}, {22, 0.00358362, 2.90781, 0.0439095, 7.80201}, {23,    0.00353606, 2.93743, 0.0254055, 7.91445}, {24, 0.00350441, 2.9569,    0.0112019, 7.99332}, {25, 0.00348267, 2.96992, 4.2709*10^-28,    8.05004}, {26, 0.00350619, 2.95655, 0.0140871, 7.98594}, {27,    0.00354397, 2.9359, 0.0380519, 7.88204}, {28, 0.0036054, 2.90368,    0.077481, 7.71557}, {29, 0.00371579, 2.84915, 0.145356,    7.43302}, {30, 0.00384706, 2.78696, 0.22453, 7.10949}, {31,    0.00402225, 2.70695, 0.319264, 6.71886}, {32, 0.00425262, 2.60492,    0.42526, 6.26836}, {33, 0.00451347, 2.4927, 0.533519, 5.80028}, {34,    0.00484984, 2.35888, 0.635259, 5.31261}, {35, 0.0052487, 2.21331,    0.726175, 4.82797}, {36, 0.00569123, 2.06324, 0.807586,    4.35526}, {37, 0.00625698, 1.90488, 0.858761, 3.92207}, {38,    0.00689091, 1.74683, 0.894649, 3.51698}, {39, 0.00759815, 1.59081,    0.915479, 3.14207}, {40, 0.00847396, 1.44051, 0.907596,    2.82513}, {41, 0.00943069, 1.29475, 0.890287, 2.53427}, {42,    0.0105185, 1.15519, 0.860229, 2.27889}, {43, 0.0117991, 1.02388,    0.81632, 2.06547}, {44, 0.0131859, 0.897942, 0.767916,    1.87227}, {45, 0.0147797, 0.780792, 0.713042, 1.70999}, {46,    0.0165753, 0.670983, 0.65441, 1.57258}, {47, 0.0184995, 0.565447,    0.594737, 1.44957}, {48, 0.0207039, 0.467657, 0.533712,    1.35086}, {49, 0.0230828, 0.374668, 0.47279, 1.26641}, {50,    0.025591, 0.285255, 0.412327, 1.1928}, {51, 0.0283735, 0.201725,    0.353629, 1.13931}, {52, 0.0312372, 0.119185, 0.295722,    1.09523}, {53, 0.0341712, 0.0377658, 0.238978, 1.06272}, {54,    0.0370919, -0.0411159, 0.184837, 1.04753}, {55, 0.03991, -0.118284,    0.132156, 1.04359}, {56, 0.0424219, -0.189196, 0.0842067,    1.05721}, {57, 0.0443678, -0.245829, 0.0451427, 1.09405}, {58,    0.0458307, -0.287877, 0.0134487, 1.15053}, {59,    0.0461722, -0.273939, 0.00724523, 1.25192}, {60, 0.04547, -0.189799,    0.029489, 1.40789}, {61, 0.0439536, -0.040825, 0.0760268,    1.61787}, {62, 0.0410509, 0.287135, 0.188407, 1.98092}, {63,    0.0374884, 0.737128, 0.339519, 2.48104}, {64, 0.0334165, 1.32035,    0.529929, 3.15253}, {65, 0.0292259, 2.16715, 0.792678,    4.24807}, {66, 0.0249774, 3.20952, 1.09423, 5.70677}, {67,    0.0209618, 4.54328, 1.4547, 7.76466}, {68, 0.0175535, 6.37734,    1.90226, 10.9599}, {69, 0.0142979, 8.71509, 2.3962, 15.3082}, {70,    0.0116484, 11.9196, 2.96614, 21.8363}, {71, 0.00952234, 16.4455,    3.46263, 31.8198}, {72, 0.00756156, 22.4422, 3.69173, 45.7099}, {73,    0.00637376, 29.2974, 3.10612, 62.8753}, {74, 0.00557852, 35.9338,    1.7877, 80.5131}, {75, 0.0050232, 41.7985, 8.59236*10^-27,    96.93}, {76, 0.00564134, 35.4285, 2.17511, 78.8748}, {77,    0.00664996, 27.396, 4.4568, 56.9122}, {78, 0.00830127, 18.7827,    5.93387, 34.9235}, {79, 0.0112518, 12.1619, 5.34133, 20.6996}, {80,    0.0147477, 7.27342, 4.38667, 11.0649}, {81, 0.0192714, 4.31069,    3.28923, 6.07815}, {82, 0.0249166, 2.64861, 2.36017, 3.78892}, {83,    0.0310646, 1.44104, 1.61259, 2.25868}, {84, 0.038089, 0.763281,    1.11354, 1.51843}, {85, 0.0455155, 0.323334, 0.756884,    1.08172}, {86, 0.0530392, -0.00833097, 0.480004, 0.764547}, {87,    0.0602388, -0.191606, 0.314908, 0.599}, {88, 0.0669456, -0.322307,    0.19112, 0.476188}, {89, 0.0729913, -0.407595, 0.101166,    0.385506}, {90, 0.0773187, -0.422702, 0.0563086, 0.338125}, {91,    0.0808823, -0.415833, 0.0252911, 0.301559}, {92,    0.0833385, -0.387366, 0.00888385, 0.276938}, {93,    0.0845245, -0.347873, 0.00355736, 0.262038}, {94,    0.085323, -0.310296, 0.000716217, 0.249179}, {95,    0.0854916, -0.278922, 0.00021299, 0.239806}, {96,    0.0853257, -0.253975, 0.000358958, 0.232963}, {97,    0.0851545, -0.232974, 0.000267074, 0.227071}, {98,    0.0848481, -0.218693, 0.000354803, 0.223956}, {99,    0.084646, -0.209427, 0.000303089, 0.222006}, {100,    0.0846189, -0.204535, 3.2539*10^-31, 0.220639}, {101,    0.084646, -0.209427, 0.000303089, 0.222006}, {102,    0.0848481, -0.218693, 0.000354803, 0.223956}, {103,    0.0851545, -0.232974, 0.000267074, 0.227071}, {104,    0.0853257, -0.253975, 0.000358958, 0.232963}, {105,    0.0854916, -0.278922, 0.00021299, 0.239806}, {106,    0.085323, -0.310296, 0.000716217, 0.249179}, {107,    0.0845245, -0.347873, 0.00355736, 0.262038}, {108,    0.0833385, -0.387366, 0.00888385, 0.276938}, {109,    0.0808823, -0.415833, 0.0252911, 0.301559}, {110,    0.0773187, -0.422702, 0.0563086, 0.338125}, {111,    0.0729913, -0.407595, 0.101166, 0.385506}, {112,    0.0669456, -0.322307, 0.19112, 0.476188}, {113,    0.0602388, -0.191606, 0.314908, 0.599}, {114,    0.0530392, -0.00833097, 0.480004, 0.764547}, {115, 0.0455155,    0.323334, 0.756884, 1.08172}, {116, 0.038089, 0.763281, 1.11354,    1.51843}, {117, 0.0310646, 1.44104, 1.61259, 2.25868}, {118,    0.0249166, 2.64861, 2.36017, 3.78892}, {119, 0.0192714, 4.31069,    3.28923, 6.07815}, {120, 0.0147477, 7.27342, 4.38667,    11.0649}, {121, 0.0112518, 12.1619, 5.34133, 20.6996}, {122,    0.00830127, 18.7827, 5.93387, 34.9235}, {123, 0.00664996, 27.396,    4.4568, 56.9122}, {124, 0.00564134, 35.4285, 2.17511,    78.8748}, {125, 0.0050232, 41.7985, 5.2584*10^-27, 96.93}, {126,    0.00557852, 35.9338, 1.7877, 80.5131}, {127, 0.00637376, 29.2974,    3.10612, 62.8753}, {128, 0.00756156, 22.4422, 3.69173,    45.7099}, {129, 0.00952234, 16.4455, 3.46263, 31.8198}, {130,    0.0116484, 11.9196, 2.96614, 21.8363}, {131, 0.0142979, 8.71509,    2.3962, 15.3082}, {132, 0.0175535, 6.37734, 1.90226, 10.9599}, {133,    0.0209618, 4.54328, 1.4547, 7.76466}, {134, 0.0249774, 3.20952,    1.09423, 5.70677}, {135, 0.0292259, 2.16715, 0.792678,    4.24807}, {136, 0.0334165, 1.32035, 0.529929, 3.15253}, {137,    0.0374884, 0.737128, 0.339519, 2.48104}, {138, 0.0410509, 0.287135,    0.188407, 1.98092}, {139, 0.0439536, -0.040825, 0.0760268,    1.61787}, {140, 0.04547, -0.189799, 0.029489, 1.40789}, {141,    0.0461722, -0.273939, 0.00724523, 1.25192}, {142,    0.0458307, -0.287877, 0.0134487, 1.15053}, {143,    0.0443678, -0.245829, 0.0451427, 1.09405}, {144,    0.0424219, -0.189196, 0.0842067, 1.05721}, {145, 0.03991, -0.118284,    0.132156, 1.04359}, {146, 0.0370919, -0.0411159, 0.184837,    1.04753}, {147, 0.0341712, 0.0377658, 0.238978, 1.06272}, {148,    0.0312372, 0.119185, 0.295722, 1.09523}, {149, 0.0283735, 0.201725,    0.353629, 1.13931}, {150, 0.025591, 0.285255, 0.412327,    1.1928}, {151, 0.0230828, 0.374668, 0.47279, 1.26641}, {152,    0.0207039, 0.467657, 0.533712, 1.35086}, {153, 0.0184995, 0.565447,    0.594737, 1.44957}, {154, 0.0165753, 0.670983, 0.65441,    1.57258}, {155, 0.0147797, 0.780792, 0.713042, 1.70999}, {156,    0.0131859, 0.897942, 0.767916, 1.87227}, {157, 0.0117991, 1.02388,    0.81632, 2.06547}, {158, 0.0105185, 1.15519, 0.860229,    2.27889}, {159, 0.00943069, 1.29475, 0.890287, 2.53427}, {160,    0.00847396, 1.44051, 0.907596, 2.82513}, {161, 0.00759815, 1.59081,    0.915479, 3.14207}, {162, 0.00689091, 1.74683, 0.894649,    3.51698}, {163, 0.00625698, 1.90488, 0.858761, 3.92207}, {164,    0.00569123, 2.06324, 0.807586, 4.35526}, {165, 0.0052487, 2.21331,    0.726175, 4.82797}, {166, 0.00484984, 2.35888, 0.635259,    5.31261}, {167, 0.00451347, 2.4927, 0.533519, 5.80028}, {168,    0.00425262, 2.60492, 0.42526, 6.26836}, {169, 0.00402225, 2.70695,    0.319264, 6.71886}, {170, 0.00384706, 2.78696, 0.22453,    7.10949}, {171, 0.00371579, 2.84915, 0.145356, 7.43302}, {172,    0.0036054, 2.90368, 0.077481, 7.71557}, {173, 0.00354397, 2.9359,    0.0380519, 7.88204}, {174, 0.00350619, 2.95655, 0.0140871,    7.98594}, {175, 0.00348267, 2.96992, 4.34023*10^-27, 8.05004}, {176,    0.00350441, 2.9569, 0.0112019, 7.99332}, {177, 0.00353606, 2.93743,    0.0254055, 7.91445}, {178, 0.00358362, 2.90781, 0.0439095,    7.80201}, {179, 0.00366125, 2.85969, 0.0685708, 7.63264}, {180,    0.0037445, 2.80767, 0.0891022, 7.46372}, {181, 0.0038446, 2.74659,    0.107359, 7.27855}, {182, 0.003962, 2.67731, 0.122165,    7.08088}, {183, 0.00408066, 2.60798, 0.130038, 6.89764}, {184,    0.00421573, 2.53408, 0.13467, 6.70861}, {185, 0.00435635, 2.46022,    0.134399, 6.52873}, {186, 0.00449348, 2.3895, 0.12767,    6.36945}, {187, 0.00464483, 2.31891, 0.12169, 6.20612}, {188,    0.00479085, 2.25265, 0.111276, 6.06199}, {189, 0.00493048, 2.19114,    0.0969574, 5.937}, {190, 0.00507624, 2.13333, 0.0868532,    5.80991}, {191, 0.00520924, 2.08121, 0.0728039, 5.70511}, {192,    0.00533414, 2.03443, 0.0587529, 5.61315}, {193, 0.005454, 1.99256,    0.0488175, 5.52469}, {194, 0.00555664, 1.95654, 0.0357567,    5.4579}, {195, 0.0056491, 1.92576, 0.026371, 5.3971}, {196,    0.00572788, 1.90041, 0.0195179, 5.34518}, {197, 0.00578611, 1.88105,    0.00995626, 5.31438}, {198, 0.00583292, 1.86694, 0.00737286,    5.28264}, {199, 0.00586038, 1.85857, 0.00496208, 5.26553}, {200,    0.00586554, 1.85613, 4.76551*10^-28, 5.26926}} 

## Color coding to get an FPT algoirthm for $k$ disjoint triangles

Consider the following problem:

Input: A graph $$G=(V,E)$$ and an integer $$k \in \mathbb{N}$$

Output: Are there $$k$$ vertex-disjoint triangles in $$G$$?

Assume we want to use color coding to develop an FPT Algorithm for that, as done here (starting from slide 60). The reference material proposes the following method:

1. Choose a random coloring $$V \rightarrow [3k]$$
2. Check if there is a colorful solution where the $$3k$$ vertices of the $$k$$ triangles use distinct colors.

For 2. it proposes this, amongst others, this method:

Try every permutation $$\pi$$ of $$[3k]$$ and check if there are triangles with colors $$(\pi(1), \pi(2), \pi(3)), (\pi(4),\pi(5),\pi(6), \dots)$$

I don’t understand why we have to check every permutation $$\pi$$ of the colors. Wouldn’t it be enough to just to check each triple of vertices, see if there are a triangle and if so, only count this triangle if it only uses colors we have not seen before? So like so:

1. For each triple $$x,y,z \in V$$:
2. If $$x,y,z$$ form a triangle and colors $${c(x),c(y),c(z)}$$ not in colors_seen_so_far:

2.1 colors_seen_so_far += $$\{c(x), c(y), c(z)\}$$

2.2 num_triangles += 1

where we initialize colors_seen_so_far = $$\emptyset$$ and num_triangles = $$0$$

## Why can I not adjust the point color? It just goes black

Here is my code here.

How to make these 2 points Blue and Orange respectively?

Manipulate[  pp = ParametricPlot[{{r1 Cos[Min[w1 x, 2 Pi]],       r1 Sin[Min[w1 x, 2 Pi]]},     {r1 Cos[w1 x] + r2 Cos[w2 x], r1 Sin[w1 x] + r2 Sin[w2 x]}},    {x, 0, t}, PlotRange -> 10 {{-1, 1}, {-1, 1}},     AxesLabel -> {"Time"},    PlotStyle -> {Automatic, Red}, BaseStyle -> Thick];  Legended[   Show[pp, Epilog -> {Black, AbsolutePointSize[5],       Point@GraphicsMeshFindIntersections[pp[[1]]],      PointSize[Large], {Blue, Orange},       Point[{{r1 Cos[w1 t],          r1 Sin[w1 t]}, {r1 Cos[w1 t] + r2 Cos[w2 t],          r1 Sin[w1 t] + r2 Sin[w2 t]}}]}],   LineLegend[{ColorData[97]@1, Red, Blue, Orange},    {"Earth Trajectory", "Moon Trajectory", "Earth", "Moon"},    Joined -> {True, True, False, False},     LegendMarkers -> {None, None, "Point", "Point"}]],  {pp, None},  {{t, 1, "Time"}, 0.01, 10 Pi, 0.01},  {{w1, 1, "Angular Velocity"}, 0.2, 5, 0.01},  {{r1, 2, "Radius"}, 0.2, 10, 0.01},  {{w2, 1, "Moon Angular Velocity"}, 0.2, 5, 0.01},  {{r2, 2, " Moon Radius"}, 0.2, 10, 0.01},  TrackedSymbols :> {t, w1, r1, w2, r2}] 

## How to tell whether should I color the edges or the vertices?

Knowing that I am dealing with an algorithmic task that requires usage of graph coloring, how can I tell whether I should color the vertices instead of the edges, or vice versa?

Is there any general shortcut to determine this? I am talking about basic greedy algorithms problems, nothing fancy.

Thanks!

## How to change all existing post title and content’ color

A customer has a WordPress blog. Last week, it looked normal. Now, suddenly all the post title and content’s font color changed into white. Not sure why. Still using the same theme, though.

This makes reading them veerryy hard. How to revert the change?

## How was the four color theorem proved using brute-force search?

I recently learned some graph theory in Discrete Structures for Computer Science, we learned about the Four Color theorem, I realize there is a mathematical proof for this topic, but how was it initially proved using computation 50 years ago?

I’m trying to change a hover color of a menu link element. Normally this is really easy, but on this projet i’m not able to do it.

site : http://mv.gr3g.ca login : valentine passwd : mas2019

I need to change the hover color of “RESERVER” button ( pink button in right header menu ) to another color.

I have tryed tons of CSS edit, no one works…

I’ll really apreciate any help for this !

I am having some issues with a project alert colors.

I am having two cases that starts an alert.

One is if the value is over 40 and one is over 45.

Reaching the 40 value is a really bad thing and reaching 45 is even worse.

The problem is that I cannot use orange for over 40 as it is really important and needs action to be taken immediately.

Currently I use light red and hard red but I am afraid that they do not differentiate well enough.